Linearity in Deng entropy

Abstract

Linearity is considered as a fundamental property of significant importance in numerous domains. A linear mathematical expression is clear, concise, and convenient for solving problems, making it a valuable tool for approximating complex issues. In recent years, Deng entropy has been proposed as a generalization of Shannon entropy, applied to measure the uncertainty degree of the mass function in the power set. There are two main contributions in this paper. One is that the linearity can be observed in Deng entropy. We present a set of specific mass functions named power assigned mass function (PAMF), which could generate linear type Deng entropy (LTDE). The other is that we find the slope is nothing else but the information fractal dimension of mass function. Moreover, we discover that for any given slope within the range of 0 to ln3ln2, at least one mass function that yields Deng entropy corresponding to the given slope can be derived through the mass function generator (MFG), in a strict linear way. Some proofs, numerical examples, discussions and an error analysis are provided to validate the effectiveness of our findings.